You really don’t want to “maintain” eye contact. An intense, unbroken gaze is discomforting for both parties.
Instead, establish eye contact and hold it briefly, until you’ve made a connection and let the person know that s/he has your attention. Then, let your eyes wander down or to the side as you listen; you’ll have a thoughtful appearance. Return to eye contact when you respond, but, again, don’t linger for too long. It isn’t natural to drill someone with nonstop eye contact, and people who do so come across as creepy.
Try practicing this technique, and you’ll likely find it very easy. If you’re still unsettled by looking directly into someone eyes, look at the top of the person’s nose, between his/her eyes, instead.